Try to activate netbios on your linux box, most of the time the computer's name is obtained by netbios when on a network without DNS server.
You may also be able to setup a DNS and to get host name from IP and the contrary, but I don't think this will show up in your router.
Other way to do so, give the same IP to the same host each time via DHCP with the NIC mac address, most of the routers are able to do it. That way you keep your setting in mind and you won't have to seek who is who. I you are lucky, this will even show the names up on your router, but this doesn't work with my netgear so...
Can you explane your forwarding problem and why you wan't it ? Maybe we can help on this.